I guess you want export vector data to Illustrator. This way is quite limited. If you ´re talking about UVs PDF is the way to go. And there´s the AutoCAD Interchange File (dxf) format which loads in LibreOffice for example (strange culling though).
As I don´t use AI I can´t say much about it.
Can you be more specific about what you´re trying probably?
If you mean to export a resulting picture as vector graphics, the answer is a simple no.
Out of the box I wouldn't know of any 3d package that has something like this incorporated. In some cases there were add-ons available who could do this to a certain degree. A full vector scalable pic in photo-quality is not possible (even those illustrator pictures that are as good as any photo-real 3d-render are no good if you blow them up (even as vector-graphics)).
What you can do is rendering an image in a toon style (the less colors the better) and then use 'image trace' (I believe it's called like that in the English version of illustrator. In the German one it's 'bildnachzeichner').
Of course the tool is limited but if you have something like a logo or another easy graphic you can create a very good version of it just with the tracer. It's a big time-saver, but works best with black and white (ideally really only those 2 colors. So it could be a help to work on the pic in photoshop first, like getting an 'edge only'-version first).